請問這題怎麼算

9. A rectangle is inscribed in a right triangle, as 000,00 shown in the accompanying figure. If the triangle 0 has sides of length 5, 12, and 13, what are the

想請教這一題微積分，謝謝！

2. (8%) Consider a real numbers and suppose that lim x→0√√x+s4-s² find s (there are two possible answers). = 3,

請教這題a,b小題 不知道怎麼列式子

4.21. Suppose that P{X=a}=p, P{X=b} = 1 - p (a) Show that X-b is a Bernoulli random variable. (b) Find Var(X).

想請問這題的(b)怎麼解！

Question 3: If f(x)=x³+3x+1, evaluate (a) f'(2) and (b) (-¹)(15). Sele

想請問紅色的地方要怎麼變藍色的

EXAMPLE 3 Solution We differentiate the equation implicitly. (AS) ² = x² + sin.xy d VIR SY d (²) - (x²)+(sin xy) = dx dx Find dy/dx if y² = x² + sinxy (Figure 3.31). d dx dy dx 2y = d 2x + (cos xy) (xy) dx ansa to along or see anuar Differentiate both sides with respect to x... ... treating y as a function of x and using the Chain Rule.

請問有人知道怎麼算嗎？拜託了🙏

11. [-/6 Points] DETAILS Find the constants a and b such that the function is continuous on the entire real line. a = b = LARCALC12M 1.4.073. 5, f(x) = ax + b, -5, 13 X ≤-2 -2<x<3 X23

請問這題要怎麼算～

1 89. Let f be a function such that f'(x): If 1 + x² 0₁5 2 LIFE AND Qurbliet 1 + x² dig(x) = f(2x + 1), what is g'(x)?sup inslissxs) =

想問第4題畫線處 分母(tan²x)-1 =(sin²x/cos²x)-1 =(sin²x-cos²x)/cos²x 為什麼把1/cos²x移到分子以後 分母不是sin²x-cos²x ? 感謝！

x² Example 4 Find lim x 0 sec X 1 SOLUTION The evaluation of this limit requires a little imagination. Since both the numerator and denominator tend to zero as x tends to zero, it is not clear what happens to the fraction. However, we can rewrite the fraction in a more amenable form by multiplying both numerator and denominator by sec x + 1. x2 x² sec x 1 lim x-0 secx 1 - = = x2 sec x 1 - x² (secx + 1) sec² x 1 lim (sin x-0 sin x sec x + 1 sec x + 1) - = Since each of these factors has a limit as x tends to 0, the fraction we began with has a limit: = x² (secx + 1) tan² x - 1 x² cos²x(secx + 1) sin² X 2 (*) ² (cos²x)(secx + 1). 2 ·lim cos²x lim (secx + 1) = (1)(1)(2) = 2. x→0 x ●

第一行是題目 第二行是給的詳解 我從第一步就不懂 為什麼要假設成L?🤨 後面也看不懂QWQ

Question Limit. 4. Find the humber c such that lim 3x²+CX+c+3 X-7-2 X²+X-2 exists and evaluate this limit. lim A = Suppose X+2+x²+x-2² = L. We have that lim (3x+exto+ 3) = lim (2xxxx112 x (x²7x²)) X7-2 x=-2 X+X-2 3x²+x+c+3 = ( Lim Xxx-9²³) x (&im₂ (X+X-2)) = Lx0=0 X-7-2 => 3x(-2)² + cx (-2) + C+3=15-C=O=> C=15

請問第41題這種類型的題目要怎麼解🙏🙏

41-44 Use implicit differentiation to find az/ax and az/ay. .2 41. x² + 2y² + 3z² = 1 (42. x² - y² + z² – 2z = 4 (43) e² = xyz 44.) yz + x ln y = z²